2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166392If two distance-3 codes have the same neighborhood, then each of them is called a mobile set. In the (4k+3)-dimensional binary hypercube, there exists a mobile set of cardinality 2*6^k that cannot be split into mobile sets of smaller cardinalities or represented as a natural extension of a mobile set in a hypercube of smaller dimension. Keywords: mobile set; 1-perfect code.9p., in Russian (English version will be finished later)CombinatoricsInformation Theory05B99; 94B25text